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We have demonstrated a straightforward strategy to realize magnetic field enhancement through diffraction coupling of magnetic plasmon (MP) resonances by embedding the metamaterials consisting of a planar rectangular array of U-shaped metallic split-ring resonators (SRRs) into the substrate. Our method provides a more homogeneous dielectric background allowing stronger diffraction coupling of MP resonances among SRRs leading to strong suppression of the radiative damping. We observe that compared to the on-substrate metamaterials, the embedded ones lead to a narrow-band hybridized MP mode, which results from the interference between MP resonances in individual SRRs and an in-plane propagating collective surface mode arising from light diffraction. Associated with the excitation of this hybridized MP mode, a twenty-seven times enhancement of magnetic fields within the inner area of the SRRs is achieved as compared with the pure MP resonance. Moreover, we also found that besides the above requirement of homogeneous dielectric background, only a collective surface mode with its magnetic field of the same direction as the induced magnetic moment in the SRRs could mediate the excitation of such a hybridized MP mode.
© 2015 Optical Society of America
1. Introduction
Metallic nanoparticles have attracted considerable interest because of their remarkable optical properties [1], which are determined by the localized surface plasmon (SP) resonances [2,3 ]. The localized SP resonances can induce strongly enhanced electric fields on the surfaces of the metallic nanoparticles. Such enlarged electric fields can lead to many applications such as surface-enhanced Raman spectroscopy [4,5 ], plasmonic sensor [6], optical antennas [7], and optical tweezers [8]. However, the linewidths of the particle SP resonances are usually broad due to the short lifetimes of the emissive plasmons caused by a rapid depletion of the plasmon energy [9], which will limit their applications in some cases. Now recent work has shown that the plasmon linewidth of metallic nanoparticles could be controlled in hybrid plasmonic-photonic systems formed by patterning nanoparticles into one- or two-dimensional (2D) arrays in a symmetric dielectric environment [10–16 ] or placing periodic arrays of nanoparticles on a dielectric waveguide [17]. In the former case, an extremely narrow-band plasmon mode, caused by the interaction of particle SP resonances with an in-plane propagating collective surface mode (also referred to as lattice resonance) arising from light diffraction, was predicted [10–12 ] and observed experimentally [13–16 ], when the array period is close to the particle SP resonance wavelength. And, such a hybridized plasmon mode has been used to enhance and direct fluorescent emission in periodic arrays of plasmonic nanoantennas due to its narrow bandwidth [18].
Recently, plasmonics has moved to metamaterials comprising artificial magnetic atoms like SRRs [19–23 ] and rod or cut-wire pairs [24,25 ], owing to the increasing attention towards the magnetic field enhancement with its potential applications in magnetic nonlinearity and magnetic sensors [26]. However, in light-matter interactions, the magnetic component of light generally plays a negligible role since it is very weak [27]. Therefore, it becomes quite important to seek novel methods to enhance the magnetic fields. A very important approach to enhance the magnetic fields is to pattern artificial magnetic atoms into one- or 2D arrays [28–30 ]. For example, it has been shown that MP resonances in the periodic array of metallic wire pairs can be coupled to the waveguide modes and Bloch surface waves, giving rise to an avoided crossing and the formation of hybrid MP resonances [28,29 ]. Very recently, we have theoretically shown that when the coupling took place between the MP resonances and lattice surface modes arising from the array periodicity in 2D periodic arrays of metallic rod-pairs, strongly enhanced magnetic fields could be achieved as a result of suppression of the radiation damping by electromagnetic field confinement in the ensemble plane [30]. Note that in the above work, the metallic rod-pair arrays are assumed to be surrounded by air. However, in the practice metallic nanoparticle arrays are fabricated on substrates. For light propagating above and below the substrate, this refraction index mismatch results in different phase velocities and conditions for constructive interference [31,32 ]. In other words, to realize the magnetic field enhancement via diffraction coupling of MP resonances in metamaterials, the condition of the homogeneous dielectric background must be satisfied [16]. However, to date it is still a challenge to achieve a largely homogeneous dielectric environment to overcome the large index mismatch limitation in conventional nanoparticle arrays.
In this letter, we propose and demonstrate a strategy by embedding the metamaterials consisting of 2D periodic arrays of U-shaped metallic SRRs into the substrate to realize magnetic field enhancement via the diffraction coupling of MP resonances. We observed the embedded metamaterials lead to a narrow-band hybridized MP mode with respect to the on-substrate ones, which could be ascribed to the fact that our strategy provides a more homogeneous dielectric background allowing stronger diffraction coupling among SRRs leading to strong suppression of the radiative damping. Upon the excitation of this hybridized MP mode, the maximum of magnetic field intensity is about 1753 times of the incident field. The magnetic fields for the SRRs are enhanced to nearly 27 times larger than those at the MP resonance of individual SRRs. More interestingly, we also found that besides the above requirement of homogeneous dielectric background, only a collective surface mode with its magnetic field of the same direction as the induced magnetic moment in the SRRs could mediate the excitation of such a hybridized MP mode.
2. Modeling structures
Figure 1 schematically presents the metamaterials to be studied, which are, respectively, embedded and on-substrate metamaterials consisting of 2D arrays of U-shaped Ag SRRs. In Fig. 1(a), h = 150 nm denotes the buried depth of the 2D SRR arrays beneath the silica substrate with a refractive index n = 1.45, and the structural parameters for the U-shaped Ag SRRs are set to be with the arm length and the base-line length l = 200 nm, the arm width wa = 50 nm, the base-line width wb = 100 nm, and the SRR height d = 50 nm. The coordinates are chosen such that the SRRs lie on the xy plane, with its origin located at the center of one of the SRRs. The array periods along the x and y axes are, respectively, Px and Py. The electric field Ein, magnetic field Hin, and wave vector Kin of the incident light are, respectively, along the x, y, and z axes. The real fabrication process for the proposed structure could be easily completed via using the current planar nanofabrication technique [33,34 ]. Firstly, a 2D array of U-shaped SRRs pattern is exposed by electron beam lithography (EBL). Then, masking by the e-beam resist, the U-shaped nanoholes pattern is transferred to the silica substrate by ICP dry-etching. Lastly, U-shaped Ag SRRs are formed by Ag evaporation and lift-off processes.
Fig. 1 Schematic view of the U-shaped Ag SRR arrays and the incident light polarization configuration together with a coordinate system. The periods along the x and y axes are Px and Py, respectively. The U-shaped Ag SRR array is buried beneath the silica substrate (a) and directly placed on the silica substrate (b).
The three-dimensional numerical simulations based on a commercial finite element method (Comsol Multiphysics) are used to calculate the transmission spectra and the electromagnetic field distributions of the structures. In the simulations, the periodic boundary conditions are applied to the four side boundaries located in the xz and yz planes, and the top and bottom boundaries in the xy plane are terminated with Perfectly Matched Layers to absorb reflected and transmitted light in the z-axis. The relative permittivity of Ag is described by a Drude model: ε = 1−ωp 2/[ω(ω + iτ −1)], where ωp is the plasma frequency and τ is the relaxation time related to energy loss. The parameters are taken to be ħωp = 9.2 eV and ħτ −1 = 0.02 eV [35]. In addition, on-substrate metamaterials as shown in Fig. 1(b) were also designed to compare the effect of the homogenous with inhomogeneous background on the collective surface resonances in the metamaterials.
3. Results and discussion
Figure 2(a) shows the transmission spectra of embedded and on-substrate U-shaped Ag SRR arrays. The two arrays have the same periods in both the x and y direction (Px = 400 nm and Py = 1250 nm). For the embedded array, as shown by the red solid line in Fig. 2(a), the transmittance shows two transmission resonances at 1596 nm and 1864 nm. Meanwhile, in order to exclude the influence of the diffraction within the spectral range of interest from 1000 nm to 2500 nm, we present the transmission spectrum of the embedded U-shaped Ag SRR array (Px = 400 nm and Py = 600 nm) in the bottom inset of Fig. 2 (a), from which it is seen that there is also a transmission resonance centered at 1596 nm indicated using the black arrow. Therefore, we can state that the transmission resonance at 1596 nm results from the excitation of MP resonance in individual SRRs since there exists no diffraction channel for such a periodic array. Actually, it has been shown that the broad transmission dip (labeled as dip 1) centered at λ1 = 1596 nm corresponds to the extinction resulting from the excitation of MP resonance in individual SRRs, and the relatively narrow transmission dip (labeled as dip 2) appearing at λ2 = 1864 nm is due to a hybridized MP mode arising from the strong coupling between MP resonances in individual SRRs and an in-plane propagating collective surface mode arising from light diffraction [30]. In [16], Auguié et al. have highlighted the importance of surrounding the nanoparticles by a homogeneous dielectric environment in order to obtain an effective diffraction coupling. In Fig. 2(a), we also show the transmittance calculated through a similar array directly placed on the substrate (black dotted line). As can be seen, the major difference for the on-substrate array compared to the transmittance of the embedded one is the disappearance of the hybridized MP mode as a result of the inefficient diffraction coupling in the inhomogeneous environment, and the MP resonance of the single SRRs is shifted to 1400 nm due to the reduced permittivity of the surrounding medium. Here, we stress that the embedded array is not in a fully symmetric dielectric environment. Instead, there is a big difference in refractive index between the lower layer and the upper layer of the SRR array, and this upper layer has a finite thickness of 150 nm. Therefore, the condition for the existence of the hybridized MP mode, namely, an homogeneous dielectric environment around the SRR array, is less stringent than believed [18,32 ].
Fig. 2 (a) Normal-incidence transmission spectra of on-substrate and embedded U-shaped Ag SRR arrays, the two arrays have the same periods in both the x and y direction (Px = 400 nm and Py = 1250 nm). Black dotted line represents the transmission spectrum of the on-substrate U-shaped Ag SRR array and red solid line represents the transmission spectrum of the embedded U-shaped Ag SRR array. The inset is the transmission spectrum of the embedded U-shaped Ag SRR array (Px = 400 nm and Py = 600 nm). (b) and (c) Normalized magnetic field intensity distributions (H/Hin)2 on the xoy plane for the dip 1 and the dip 2. Black solid line outlines the regions of U-shaped Ag SRRs.
Figure 2(b) shows the magnetic field distributions on the xoy plane for the resonance λ1 = 1596 nm. It is clear that the magnetic fields are highly confined in the inner area of the SRRs, which are characteristics of a MP resonance of individual metallic SRRs. In Fig. 2(c), we plot the corresponding magnetic field distributions on the xoy plane for the dip 2 resonance located at λ2 = 1864 nm. Although the field pattern is almost the same as the case shown in Fig. 2(b), the magnetic fields in the inner area of the SRRs become much stronger, with a nearly 27 times enhancement. In particular, the maximum magnetic fields is enhanced to be about 1753 times of the incident field [please see Fig. 2(c)].
In order to further get full understanding of the formation mechanisms for the narrow-band hybridized MP mode in the embedded U-shaped Ag SRR arrays, in Figs. 3(a)-3(f) we plot normalized electric (magnetic) field intensity components on the xoy plane by differentiating the x, y, and z components of the total electromagnetic fields at the dip 2 resonance. It is seen from Figs. 3(a)-3(f) that the electric (magnetic) field component of the lattice resonance mode is mainly distributed along the x (z) direction, which evidently indicates that the lattice resonance mode propagating in the y direction has an electric (magnetic) field parallel to the x (z) axis. Because the lattice resonance mode has a magnetic field of the same direction as the induced magnetic moment (along the z direction) in the Ag SRRs, it can strongly interact with the MP resonance in each metallic SRRs when grazing the metamaterial surface. Such a strong interaction can suppress radiative damping since the electromagnetic fields of the surface mode are trapped in the lattice [12,36 ], thus forming a narrow-band hybridized MP mode at the dip 2.
Fig. 3 (a)-(c) Normalized electric field intensity components (Ex/Ein)2, (Ey/Ein)2 and (Ez/Ein)2 on the xoy plane for the dip 2. (d)-(f) Normalized magnetic field intensity components (Hx/Hin)2, (Hy/Hin)2 and (Hz/Hin)2 on the xoy plane for the dip 2. (g) Normal-incidence transmission spectrum of the embedded SRR array with similar structural parameters but with different array periods (Px = 1250 nm and Py = 400 nm), in which the transmission spectrum of the embedded SRR array mentioned above (Px = 400 nm and Py = 1250 nm) is also shown for comparison purpose.
It is important to note that in the embedded U-shaped Ag SRR array investigated in Fig. 2(a), the period Px is set to be 400 nm, a value much smaller than the spectral range of interest from 1000 nm to 2500 nm. As a result, the diffraction channel in the x direction is closed and only the diffraction channel in the y direction is opened for this case. Similarly, by varying the array periods while keeping the other conditions unchanged, we have also studied other situations in which the diffraction channel along the y direction is closed but the one along the x direction is opened. Figure 3(g) shows the transmission spectrum of the embedded SRR array with similar structural parameters but with different array periods (Px = 1250 nm and Py = 400 nm), in which the transmission spectrum of the embedded SRR array investigated above (Px = 400 nm and Py = 1250 nm) is also shown for comparison purpose. As can be clearly seen in Fig. 3(g), different from the former case, the interference between two kinds of resonance modes do not lead to a narrow-band hybridized MP mode, which is due to the fact that the magnetic field of the induced surface mode propagating in the x direction is orthogonal to the induced magnetic moment (along the z direction) in the U-shaped Ag SRRs, that is, the surface mode cannot interact directly with MP resonances of individual Ag SRRs [37].
For the embedded array here, we carried out a further study on the transmission response to different buried depth. By embedding the array into the substrate with different depth (h), we obtain the interesting optical properties shown in Fig. 4(a) , in which the transmission spectrum of the on-substrate SRR array is also shown for comparison. As clearly seen in Fig. 4(a), compared with the on-substrate array, the embedded ones result in a hybridized MP mode. When h increases from 50 to 150 nm in intervals of 25 nm, the transmittance for the narrow-band hybridized MP mode shows a slightly red-shift in the spectral position, accompanied by decreased transmission intensity and linewidths. Figures 4(b)-4(f) show the magnetic field distributions on the xoy plane for the corresponding hybridized MP modes as shown by a dashed-line box in Fig. 4(a). As can be seen, the magnetic fields exhibit gradually enhanced trend with increasing h due to the reduced refraction index mismatch in the SRR array allowing stronger diffraction coupling of MP resonances among SRRs leading to strong suppression of the radiative damping. Moreover, the magnetic fields are strongly enhanced for the embedded arrays compared with the on-substrate cases [see Fig. 2(b)], which evidently shows that the embedded geometry offers great advantages over on-substrate geometry [31,32 ]. In addition, it should be noted here that if we use silicon or nonlinear materials instead of silica as substrate in this case, the large magnetic field enhancement in the dielectric medium could also be extremely attractive for photovoltaic and magnetic nonlinearity applications.
Fig. 4 (a) Normal-incidence transmission spectra of the U-shaped Ag SRR arrays (Px = 400 nm and Py = 1250 nm) embedded beneath the substrate with the buried depth h = 50 nm, 75 nm, 100 nm, 125 nm, and 150 nm, respectively, in which the transmission spectrum of the on-substrate SRR array is also shown for comparison. (b)-(f) Normalized magnetic field intensity distributions (H/Hin)2 on the xoy plane for the corresponding narrow-band hybridized MP modes as shown by a dashed-line box in (a). Black solid line outlines the regions of U-shaped Ag SRRs.
4. Conclusion
In conclusion, we have shown that by embedding the metamaterials consisting of 2D periodic arrays of U-shaped metallic SRRs into the substrate, the strongly enhanced magnetic fields can be obtained due to the diffraction coupling of MP resonances in periodic metamaterials. The effect could be attributed to the more homogeneous dielectric background present in embedded metamaterials allowing stronger diffraction coupling of MP resonances among metallic SRRs leading to a narrow-band hybridized MP mode. Moreover, we also found that besides the requirement of homogeneous dielectric background, only a collective surface mode with its magnetic field of the same direction as the induced magnetic moment in the SRRs could mediate such a coupling. Upon the excitation of this hybridized MP mode, the magnetic fields in the inner area of the SRRs can be greatly enhanced, which could find important applications in magnetic sensors or detectors, magnetic nonlinearity and devices based thereon, and inducing magnetic dipole transitions.
Acknowledgments
The authors gratefully acknowledge Professor Jianqiang Liu at Jiujiang University for helpful discussions and providing the commercial software package (COMSOL Multiphysics) based on finite-element method. This work is financially supported by the National Natural Science Foundation of China (Nos. 11304159, 11104136, 61471189, 61101012, 61372045), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Nos. 20133223120006, 20123223120003), the Natural Science Foundation of Zhejiang Province (No. LY14A040004), and the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (No. NY213023).
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